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If Sandy can afford car payments of \( \$ 270 \) per month for 4 years, what is the price of a car that she can allord now? Assume an interost rate of 72 percent HW Score: \( 66.23 \%, 30.8 \) of 69 points Sandy can afford a car that costs \( \$ \square \) or less. (Round to the nearest dollar as needed.)

Ask by Stephens Craig. in the United States
Mar 18,2025

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Sandy can afford a car priced at \$4,226 or less.

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To find out the price of the car Sandy can afford, we need to calculate the present value of the car payments. Using the formula for the present value of an annuity: \[ PV = PMT \times \left(1 - (1 + r)^{-n}\right) / r \] where \(PMT\) is the monthly payment (\$270), \(r\) is the monthly interest rate (annual interest rate of 72% divided by 12), and \(n\) is the total number of payments (4 years × 12 months = 48 payments). First, we convert the annual interest rate into a monthly rate: \[ r = \frac{0.72}{12} = 0.06 \] Now we can plug in the numbers: \[ PV = 270 \times \left(1 - (1 + 0.06)^{-48}\right) / 0.06 \] Calculating the present value gives: \[ PV = 270 \times (1 - (1.06)^{-48}) / 0.06 \approx 270 \times 15.7610 \approx 4255 \] Thus, Sandy can afford a car that costs approximately \( \$4,255 \) or less.

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